The distinction you should be making is the difference between a kennel and a boarding kennel.
I am all for freedom of speech but lets call a spade a spade and not dress it up as something it is not.
The differences between a hotel and a boarding establishment are vast as far as the legal world is concerned. Try reading the Hotel Proprietors Act.,whish does not apply to boarding establishments.
As The welfare of animals is far more important than humans,I suggest, although I have done no research, that the the difference in client protection is magnified, the animals welfare is paramount.
I would further advise if you are going to go down the route of dog hotel that you add the word private to the title.
Once you realise that hotels are different kettle of fish to boarding establishments you will then realise that you can call it what you want in the human world some of the more popular ones are Motel, Lodge and of cause my personal favorite Towers
"As far as a business being like “gamboling on the horses” is concerned, I guess it depends how fast it takes off."
History teaches you different, Foinavon is one example and a lot of dot coms although it worked for amazon it does not work for most.